Question

Two persons A and B walk round a circle whose diameter is $1.4km$. A walks at a speed of $165$ meters per minute while B walks at a speed of $110$ meters per minute. If they both start at the same time from the same point and walk in the same direction, at what interval of time would they both be at the same starting point again?

• A. $1h$
• B. $1\frac{1}{3}h$
• C. $1\frac{2}{3}h$
• D. $1\frac{1}{2}h$

Answer 1

The correct option is B $1\frac{1}{3}h$

Diameter of the circle $=1.4cm$

$\Rightarrow$ Circumference $=2\pi r$ $=2\times \frac{22}{7}\times \frac{1.4}{2}km=4.4km$

A's speed $=165m/min$

$\therefore$ Time taken by A to travel 4.4 km (4400 m)$=\frac{4400}{165}min=\frac{80}{3}min$

B's speed = 110 m/ min

$\therefore$ Time taken by B's to travel 4.4 km (4400 m) $=\frac{4400}{110}min=40min$

Required interval of time = LCM of $(\frac{80}{3},40)$

$=\frac{LCM(80,40)}{HCF(3,1)}=\frac{80}{1}min=\frac{80}{60hrs}=1\frac{1}{3}hrs$